MAT 335

Main Topics for the Final Exam

In addition to the topics listed on the Main Topics for Tests 1-3, are these:

Eigenvalues

Given a square matrix A, be able to:

• determine whether or not l is an eigenvalue of A

• determine whether or not x is an eigenvector of A

• given that l is an eigenvalue of A, find a basis for the eigenspace of A corresponding to l.

• given a square matrix A, find its eigenvalues (2x2 and 3x3 by hand)

Inner products and orthogonality

Be able to:

• find the inner product of two vectors

• find the length of a vector

• find the distance between two vectors

• determine whether two vectors are orthogonal or not

• find the projection of one vector onto another

• find the projection of a vector onto the column space of a matrix

• find the least squares solution to an inconsistent system